Unusual stability of multiply charged organo-metallic complexes

Abstract

Stabilization of multiply charged ions in the gas phase has been one of the most fundamental challenges in chemistry since it is hindered either because of fragmentation or auto-electron detachment. Closo-borane B₁₂H₁₂²⁻ is among the best known multiply charged di-anion in chemistry where the second electron is bound by 0.9 eV. We show that transition metal based organo-metallic di-anions such as Cr[BC₅(CN)₆]₂ can be even more stable than B₁₂H₁₂²⁻ where the second electron is bound by 2.58 eV. This is in contrast to C₆H₆ which is unstable even as a mono-anion. The unusual stability of the organo-metallic complex is brought about by having the added electrons simultaneously satisfy three separate electron-counting rules, namely the octet rule, the aromaticity rule, and the 18-electron rule. Mono-anionic Mn[BC₅(CN)₆]₂ which is isoelectronic with di-anionic Cr[BC₅(CN)₆]₂ is also found to be very stable. The design of unusually stable singly and multiply charged organo-metallic negative ion complexes in the gas phase opens the door to the synthesis of new salts with potential applications as organic cathodes and electrolytes in Li ion-batteries and beyond. Equally important, electron counting rules can be used effectively to guide the synthesis of electronegative species beyond super- and hyperhalogens, and hence opening the door for new oxidizing agents.

---

Over the past 30 years the study of multiply charged molecular ions has been a topic of great interest¹ not only because they enable a fundamental understanding of interstellar chemistry but also for their potential as building blocks of salts and Zintl phase compounds, fusion devices, high intensity ion sources, and use in analytic mass spectrometry of large biomolecules. Multiply charged species are commonly seen in solutions or in a condensed phase where they are stabilized either by counter-ions or interaction with the solvent molecules. Their stability in the gas phase, however, is governed by a delicate balance between the repulsive Coulomb forces and attractive interaction generated by chemical bonding and charge/induced-dipole interactions. Small multiply charged molecular negative ions in the gas phase are seldom stable due to spontaneous emission of electron (the so-called auto-detachment) or fragmentation into mono-anions. In the early 1990's observation of long-lived cluster di-anions such as C₆₀²⁻ could be explained² by the existence of substantial Coulomb barriers that hinder the emission of one of the excess electrons. More recently, electronic stability of di-anionic metal hexafluoride complexes such as ZrF₆²⁻, first predicted by theory,^3–5 has been confirmed by photoelectron spectroscopy experiments,⁶ but their thermodynamic stability is not addressed. How small a cluster can bind two extra electrons without auto-detaching or fragmenting remains an unanswered question. A classic example of a thermodynamically stable di-anion is B₁₂H₁₂²⁻. This cluster belongs to the class of closo-boranes, B_nH_n²⁻, whose stability gave rise to the Wade–Mingos rule^7–10 and B₁₂H₁₂ is the smallest cluster in this series¹¹ capable of holding on to two electrons.

In this paper we show that the di-anion of a small organometallic complex, namely Cr[BC₅(CN)₆]₂²⁻, is thermodynamically even more stable than the classic B₁₂H₁₂²⁻. This unusual stability is brought about by having the added electrons simultaneously satisfy three different electron counting rules, namely, the octet rule,^12–14 the aromaticity rule,¹⁵ and the 18-electron rule.¹⁶ Furthermore, this approach provides a recipe for designing moieties with ever-increasing electron affinities, such as superhalogens, hyperhalogens and beyond. For clarity we first define these species: in the early 1980's Gutsev and Boldyrev¹⁷ coined the word “superhalogen” to describe molecules, MX_k+1 where M is a metal atom with maximal valence k and X is a halogen atom. Since the extra electron is distributed over (k + 1) halogen atoms, the vertical detachment energy, VDE (i.e. the energy to remove the extra electron from MX_k+1 anions without changing its geometry) is larger than the electron affinity of halogen atoms. Several works over the past decade^18–21 have revealed the existence of superhalogens that contain neither a metal atom nor a halogen atom. In addition, another class of electronegative species composed of a metal atom at the core and surrounded by superhalogens, Y was discovered.²² The VDEs of the resulting species, MY_k+1, referred to as hyperhalogens, are found to be even larger than that of their superhalogen building blocks. In this paper we provide an alternate route to create the super- and hyper-halogens species that do not use metal atoms at the center surrounded by halogens or superhalogens. Instead, we use multiple electron counting rules simultaneously to achieve the same objective. This procedure not only enables us to create highly electronegative species beyond hyperhalogens, but also allows creating doubly charged anions that are thermodynamically stable, opening the door to the synthesis of a new class organo-metallic salts.

To demonstrate our procedure, we begin with a simple organic molecule, benzene (C₆H₆) whose stability is governed by the well-known aromaticity¹⁵ rule that requires (4n + 2) unbound π electrons, where n is an integer. For benzene, n = 1. Because of its stability, the electron affinity of benzene²³ is −1.14 eV, i.e. benzene is unstable as a mono-anion. However, this electron affinity can be substantially increased^24,25 if the H ligands are substituted by a more electronegative ligand, e.g. CN. Note that the electron affinity of H is 0.75 eV while that of CN is 3.86 eV.²⁶ The large electron affinity of CN arises because C needs one extra electron to fulfill its octet shell closure. The electron affinity of hexacyanobenzene [C₆(CN)₆] is 3.53 eV,^25,27 substantially higher than that of C₆H₆. Now, if one of the C atoms in cyanobenzene [C₆(CN)₆] is replaced by a B atom, BC₅(CN)₆ would need one extra electron to satisfy the aromaticity rule. Hence, it should have increased stability as a mono-anion. Indeed, this is the case and calculations show that the electron affinity of BC₅(CN)₆ is 5.87 eV,²⁴ which is larger than that of CN. Thus, BC₅(CN)₆ can be classified as a hyperhalogen. This line of reasoning can be carried one step further by constructing an organometallic complex composed of BC₅(CN)₆ moieties and a transition metal atom such that the complex would need one extra electron to satisfy a third electron counting rule, namely the 18-electron rule. Mn[BC₅(CN)₆]₂ is such a complex. With an electronic configuration of 3d⁵ 4s², Mn can contribute 7 electrons while each BC₅(CN)₆ molecule contributes 5 electrons. Thus, Mn[BC₅(CN)₆]₂ has 17 electrons, one short of fulfilling the 18-electron shell closure rule. The question then is: “Would the electron affinity of Mn[BC₅(CN)₆]₂ be higher than that of BC₅(CN)₆” ? If so, this would provide a pathway to create electronegative clusters beyond hyperhalogens. We name such moieties as super-hyperhalogens. Similarly, if Mn[BC₅(CN)₆]₂ is stable as a monoanion, Cr[BC₅(CN)₆]₂²⁻ which is isoelectronic with Mn[BC₅(CN)₆]₂⁻ should be stable as a di-anion. Using first-principles theory we show in the following sections that this indeed is the case.

Our calculations are based on the density functional theory (DFT) within the generalized gradient approximation (GGA). We used PW91 functional²⁸ for exchange-correlation potential along with effective core potential and double-numerical polarized basis set, implemented in the DMol3 code.²⁹ The geometries of clusters were fully optimized without symmetry constraints. The total energies were converged to 10⁻⁶ Hartree. Frequency analysis was performed at the same level of theory to ensure that there were no imaginary frequencies and the structures belong to a minimum in the potential energy surface. We have applied the orbital occupation at 0 K (Fermi) and evaluated the on-site charge and magnetic moment using the Hirshfeld population analysis. The stability of the anion is studied by computing the VDE which defines the energy needed to remove an electron from the negative ion complex without changing its geometry. The Electron Affinity (EA), on the other hand, is calculated as the energy difference between the ground states of the anion and the neutral.

In Fig. 1 we plot the equilibrium geometries of neutral and anionic Mn[BC₅(CN)₆]₂. The geometries of the neutral and negatively charged complexes are virtually identical and represent staggered structures. The BC₅(CN)₆ moieties are nearly planar and the Mn atom resides mid-way between the two moieties. The only difference is in the distance between the two planes, in the anion it is 0.13 Å closer than that in the neutral. This is consistent with the fact that the anion, guided by the 18-electron shell closure rule, is more stable than the neutral. We have also tried the eclipsed conformation as well as other isomers by varying the position of B. The results are given in Fig. 2. However, the geometries in Fig. 1b represent the ground state structure with the isomers in Fig. 2 lying between 0.011 and 0.022 eV higher in energy. We also calculate the binding energy between the Mn⁺ atom and BC₅(CN)₆ moieties, with E_b = −(E_{Mn[BC5(CN)6]2⁻} − E_Mn⁺ − 2E_{[BC5(CN)6]⁻})/2 = 3.1 eV, indicating strong chemical interactions between the central cation Mn and the two BC₅(CN)₆ planes.

Fig. 1 Equilibrium geometries of (a) neutral and (b) anionic Mn[BC₅(CN)₆]₂ cluster.

Fig. 2 Typical isomers of Mn[BC₅(CN)₆]₂⁻ and their relative energies with respect to the ground state shown in Fig. 1b.

The magnetic moments, charge on the Mn atom, and the vertical detachment energy (VDE) of Mn[BC₅(CN)₆]₂ are given in Table 1. The neutral cluster has a magnetic moment of 1 μ_B. In the anion, the electron spins are quenched because of the 18-electron shell closure rule. The VDE of Mn[BC₅(CN)₆]₂, namely, 6.53 eV, is marginally larger than its EA of 6.40 eV. This is consistent with the fact that there is very little change between the ground state geometries of the anion and the neutral complex. Since these values are larger than that of the electron affinity of its hyperhalogen building block, BC₅(CN)₆, we term Mn[BC₅(CN)₆]₂ as a super-hyperhalogen.

Table 1 Calculated total spin (in μ_B), charge on metal atom (in |e|), and VDE (in eV) of systems in their neutral (denoted as N), mono-anion (A), and di-anion (2A) states using DMol3 code. The 1^st and 2^nd VDE of Cr[BC₅(CN)₆]₂²⁻ correspond to the energy necessary to remove the 1^st and 2^nd electron, respectively

Systems	Spin N/A/2A	Charge Cr, Mn (N/A/2A)	VDE
			DMOL	G09
Mn[BC5(CN)6]2	1/0/-	0.17/0.09/—	6.53	6.64
[BC5(CN)6] Cr[C6(CN)6]	1/0/-	0.40/0.31/—	6.25	5.73
Cr[BC5(CN)6]2	2/1/0	0.45/0.36/0.31	2.58 (1^st) 6.05 (2^nd)	2.07 (1^st) 5.58 (2^nd)

---

To demonstrate the versatility of our approach we also consider another organometallic complex, [BC₅(CN)₆]Cr[C₆(CN)₆]. Cr, with an electronic configuration of 3d⁵ 4s¹, can contribute 6 electrons which, combined with 6-electrons from the cyanobenzene and 5 electrons from BC₅(CN)₆, constitute a 17 electron-system. Thus, [BC₅(CN)₆]Cr[C₆(CN)₆] is isoelectronic with Mn[BC₅(CN)₆]₂ and the addition of a single electron can enable it to satisfy simultaneously the 18-electron rule and the aromaticity rule, in addition to the octet rule that stabilizes CN⁻. Consequently, its anion can be expected to be very stable and its VDE can be larger than that of BC₅(CN)₆. If that were to be the case, [BC₅(CN)₆]Cr[C₆(CN)₆] like Mn[BC₅(CN)₆]₂ can also be termed as a super-hyperhalogen. In Fig. 3 we present the equilibrium geometries of neutral and anionic [BC₅(CN)₆]Cr[C₆(CN)₆] cluster. As in Mn[BC₅(CN)₆]₂ here also both the anion and neutral are structurally similar. Furthermore, BC₅(CN)₆ and C₆(CN)₆ also retain their planarity.

Fig. 3 Equilibrium geometries of (a) neutral and (b) anionic [BC₅(CN)₆]Cr[C₆(CN)₆] clusters.

The calculated VDE as well as magnetic moment of neutral and anionic [BC₅(CN)₆]Cr[C₆(CN)₆] are given in Table 1. The VDE and EA of [BC₅(CN)₆]Cr[C₆(CN)₆] are 6.25 eV and 6.22 eV, respectively. These are higher than that of the corresponding values in BC₅(CN)₆. Hence, [BC₅(CN)₆]Cr[C₆(CN)₆], as expected, is a super-hyperhalogen.

Finally, we examine if the simultaneous fulfillment of the above three electron counting rules can make the di-anion of an organometallic complex thermodynamically stable. We consider for this purpose Cr[BC₅(CN)₆]₂ cluster which is a 16-electron system. Thus, it needs two extra electrons to satisfy the octet and the 18-electron rule, as well as the aromaticity rule of the rings. Note that the di-anionic Cr[BC₅(CN)₆]₂ is isoelectronic with mono-anionic Mn[BC₅(CN)₆]₂ whose stability, as discussed earlier, has already been established. We have calculated the equilibrium geometries of neutral, mono-anionic and di-anionic Cr[BC₅(CN)₆]₂ clusters. The results are given in Fig. 4. All three geometries look similar with the exception of the distance between the two planes. The distances between two planar BC₅(CN)₆ moieties gradually decrease from neutral to di-anion, confirming that their stability increases as electrons are successively added. The binding energy between the Cr atom and BC₅(CN)₆ moieties, with E_b = −(E_{Cr[BC5(CN)6]2²⁻} − E_Cr − 2E_{[BC5(CN)6]⁻})/2 = 0.8 eV. We also calculate the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the optimized Mn[BC₅(CN)₆]₂⁻ and Cr[BC₅(CN)₆]₂²⁻ (Fig. 5). It can be seen that the HOMO (LUMO) of Mn[BC₅(CN)₆]₂⁻ is contributed by the Mn-d orbital and the BC₅(CN)₆ planes (Mn-d orbital and B atoms), while the HOMO (LUMO) of Cr[BC₅(CN)₆]₂²⁻ is from the Cr-d orbital and B atoms (BC₅(CN)₆ planes).

Fig. 4 Equilibrium geometries of (a) neutral, (b) anionic and (c) di-anionic Cr[BC₅(CN)₆]₂ clusters.

Fig. 5 Isosurface (value of 0.03 e Å⁻³) form of HOMO and LUMO of Mn[BC₅(CN)₆]₂⁻ and Cr[BC₅(CN)₆]₂²⁻.

The VDE and EA of Cr[BC₅(CN)₆]₂ is 6.05 eV and 6.00 eV respectively which already makes this cluster a super-hyperhalogen, even though the mono-anion is a 17-electron system. When the second electron is attached, the energy of the di-anion is lowered by another 2.58 eV from that of its mono-anion, confirming its thermodynamic stability. In contrast, the second electron affinity of the well-known B₁₂H₁₂²⁻ is 0.9 eV.³⁰ Thus, the di-anion of Cr[BC₅(CN)₆]₂ is even more stable than B₁₂H₁₂²⁻! This is clearly due to the simultaneous fulfillment of three separate electron shell closure rules.

To ensure that the extraordinary stability of this di-anion moiety is not affected by our computational procedure we have repeated the calculations of Cr[BC₅(CN)₆]₂ using two more computer codes, Gaussian (G09W)³¹ and Vienna Ab initio Simulation Package (VASP).³² The former uses Gaussian basis functions while the latter uses plane waves with cut-off energy of 400 eV. For G09W calculations the total energies and equilibrium geometries of the most stable anions and corresponding neutral molecules were calculated using Density Functional Theory (DFT) and B3LYP hybrid functional³³ for exchange-correlation potential along with the 6-31+G(d) basis set for B, C, N and SDD basis set for Cr and Mn. For VASP calculations PBE functional³⁴ is used with a vacuum space of 15 Å applied along all three directions in order to avoid interactions between nearest neighbor images. The reason for our choice of different exchange-correlation energy functionals from that used in the DMol3 code is to test if our results are influenced by the choice of a particular functional. For cluster calculations, only the point is used to represent the reciprocal space. Convergence criteria for total energy and force components are set to 10⁻⁴ eV and 0.01 eV Å⁻¹, respectively.

The VDE values of Mn[BC₅(CN)₆]₂⁻ and [BC₅(CN)₆]Cr[C₆(CN)₆]⁻ calculated at the B3LYP level using Gaussian 09 code are 6.64 and 5.73 eV, respectively. The first and second VDE of Cr[BC₅(CN)₆]₂²⁻ computed at the same level as above are, respectively, 2.07 and 5.58 eV. The results are given in Table 1. These values are about 0.5 eV lower than those obtained using the numerical basis set and the DMol3 code. It is to be noted that results obtained at the B3LYP level of theory with Gaussian basis sets are numerically more reliable than those at the DMol3 level of theory as it takes an extended basis to represent negative ions properly. Similarly, the first and second VDE of Cr[BC₅(CN)₆]₂²⁻ obtained using plane wave basis sets and the VASP code are respectively 1.93 and 5.92 eV. While the former is close to the Dmol3 result, the second is closer to the Gaussian 09 result. What is most important is that the results are consistent with each other as far as the stability of the di-anion is concerned, although the numerical results vary somewhat from one method to another. Thus, our conclusion that Cr[BC₅(CN)₆]₂ is a super-hyperhalogen and its di-anion is thermodynamically stable remains robust!

To further confirm the stability of the di-anion we have carried out a 5 ps ab initio molecular dynamics simulation at 1 fs interval at 300 K by using DMol3 code. Nosé–Hoover thermostat³⁵ is used to maintain the temperature during the simulation. The corresponding temperature and potential energy plots are given in Fig. 6 for three different snapshots (0 fs, 500 fs and 5000 fs). During the simulation only a slight structural distortion is seen mainly in the CN ligands, but overall the structure and stability of Cr[BC₅(CN)₆]₂²⁻ remain unaffected. We also simulate infrared and Raman spectra of Cr[BC₅(CN)₆]₂²⁻ cluster (Fig. 7) so that they can motivate future experiments and validate the computed structures.

Fig. 6 Molecular dynamics simulation of Cr[BC₅(CN)₆]₂²⁻ cluster.

Fig. 7 Infrared and Raman spectra of Cr[BC₅(CN)₆]₂²⁻ cluster.

In summary, we have shown that transition metal elements such as Mn and Cr play an important role in the stability of organo-metallic complexes and that electron counting rules can be effectively used to design highly stable negatively charged molecular species. The electron affinities of these complexes can be rather high and moieties beyond hyperhalogens can be designed. Equally important, organo-metallic di-anions, thermodynamically even more stable than well-known B₁₂H₁₂²⁻, can be created. Our method also provides an alternate path to design and synthesize highly electronegative species. Instead of the past practice of varying the number of halogen or superhalogen ligands until their number exceeds the maximal valence of a core metal atom, we accomplish the same goal by satisfying simultaneously multiple electron counting rules. That a single electron can be used to simultaneously fulfill three different electron counting rules provides a unique pathway to design multiply charged anions, suitable for making novel organo-metallic salts. Use of such salts as electrolytes or cathodes can open the door to a new generation of metal ion-batteries. Our numerical method has predictive capability and we hope that these results will guide experimentalists in the synthesis highly electronegative organo-metallic complexes. We should point out that organometallic complexes in the gas phase have been experimentally synthesized and studied in the gas phase for many years³⁶ and similar techniques can be used to study the stable dianions predicted in this work.

Acknowledgements

This work is supported in part by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02-96ER45579. Resources of the National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231 is also acknowledged.

References

1. A. Dreuw and L. S. Cederbaum, Chem. Rev., 2002, 102, 181–200.
2. C. Jin, R. L. Hettich, R. N. Compton, A. Tuinman, A. Derecskei-Kovacs, D. S. Marynick and B. I. Dunlap, Phys. Rev. Lett., 1994, 73, 2821–2824.
3. A. I. Boldyrev and J. Simons, J. Chem. Phys., 1992, 97, 2826–2827.
4. M. Gutowski, A. I. Boldyrev, J. V. Ortiz and J. Simons, J. Am. Chem. Soc., 1994, 116, 9262–9268.
5. M. Gutowski, A. I. Boldyrev, J. Simons, J. Rak and J. Blazejowski, J. Am. Chem. Soc., 1996, 118, 1173–1180.
6. X.-B. Wang and L.-S. Wang, J. Phys. Chem. A, 2000, 104, 4429–4432.
7. K. Wade, J. Chem. Soc. D, 1971, 792–793.
8. K. Wade, Adv. Inorg. Chem. Radiochem., 1976, 18, 1–66.
9. D. M. P. Mingos, Acc. Chem. Res., 1984, 17, 311–319.
10. D. M. P. Mingos and R. L. Johnston, Struct. Bond., 1987, 68, 29–87.
11. M. L. McKee, Z. X. Wang and P. V. Schleyer, J. Am. Chem. Soc., 2000, 122, 4781–4793.
12. R. Abegg, Zeitschrift für anorganische Chemie, 1904, 39, 330–380.
13. G. N. Lewis, J. Am. Chem. Soc., 1916, 38, 762–785.
14. I. Langmuir, J. Am. Chem. Soc., 1919, 41, 868–934.
15. E. Hückel, Z. Phys., 1931, 70, 204–286.
16. I. Langmuir, Science, 1921, 54, 59–67.
17. G. Gutsev and A. I. Boldyrev, Chem. Phys., 1981, 56, 277–283.
18. H. J. Zhai, L. M. Wang, S. D. Li and L. S. Wang, J. Phys. Chem. A, 2007, 111, 1030–1035.
19. M. Gotz, M. Willis, A. Kandalam, G. G. Gantefor and P. Jena, ChemPhysChem, 2010, 11, 853–858.
20. B. Pathak, D. Samanta, R. Ahuja and P. Jena, ChemPhysChem, 2011, 12, 2423–2428.
21. D. Samanta, M. M. Wu and P. Jena, Inorg. Chem., 2011, 50, 8918–8925.
22. M. Willis, M. Gotz, A. K. Kandalam, G. Gantefor and P. Jena, Angew. Chem., Int. Ed., 2010, 49, 8966–8970.
23. P. D. Burrow, J. A. Michejda and K. D. Jordan, J. Chem. Phys., 1987, 86, 9–24.
24. S. Giri, B. Z. Child and P. Jena, ChemPhysChem, 2014, 15, 2903–2908.
25. B. Z. Child, S. Giri, S. Gronert and P. Jena, Chem.–Eur. J., 2014, 20, 4736–4745.
26. S. E. Bradforth, E. H. Kim, D. W. Arnold and D. M. Neumark, J. Chem. Phys., 1993, 98, 800–810.
27. X. Zhang, Q. Li, J. B. Ingels, A. C. Simmonett, S. E. Wheeler, Y. Xie, R. B. King, H. F. Schaefer III and F. A. Cotton, Chem. Commun., 2006, 758–760.
28. Y. Wang and J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 44, 13298–13307.
29. B. Delley, J. Chem. Phys., 1990, 92, 508–517.
30. S. Li, M. Willis and P. Jena, J. Phys. Chem. C, 2010, 114, 16849–16854.
31. M. J. Frisch, et al., GAUSSIAN 09, Revision B.01, Gaussian, Inc., Wallingford, CT, 2010.
32. G. Kresse and J. Furthmuller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
33. A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652.
34. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
35. S. Nosé, J. Chem. Phys., 1984, 81, 511–519.
36. T. Kurikawa, H. Takeda, M. Hirano, K. Judai, T. Arita, S. Nagao, A. Nakajima and K. Kaya, Organometallics, 1999, 18, 1430–1438.

---